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------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/master08.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/preview.wmf Content-Transfer-Encoding: base64 Content-Type: image/x-wmf AQAJAAADygAAAAUAIQAAAAAABAAAAAMBCAAFAAAACwIAAAAABQAAAAwC7wLpAwMAAAAeAAcAAAD8 AgAA////AAAABAAAAC0BAAAIAAAA+gIFAAAAAAD///8ABAAAAC0BAQAMAAAAQAkhAPAAAAAAAAAA 7wLpA/////8IAAAA+gIAAAAAAAAAAAAABAAAAC0BAgAEAAAALQEAAAQAAAAnAf//HAAAAPsC1P8A AAAAAACQAQAAAAAAQAAiQXJpYWwAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAEAAAALQEDAAQA AAAuARgABAAAAAIBAQAFAAAACQIAAAACIQAAADIKMABHAREAAABSYWRpY2FsIEVxdWF0aW9ucwAg ABgAGAALABYAGAAKAA0AHQAZABkAGAAMAAsAGQAYABYABAAAAC4BAAAcAAAA+wIQAAcAAAAAALwC AAAAAAECAiJTeXN0ZW0AAAAAAAAYAAAAHLETAAEAAADkBAAAAAAAAAQAAAAtAQQABAAAAPABAwAD AAAAAAA= ------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/pres.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0045.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Radical Equations
Radical Equation= s
------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0064.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Radical Equations
Rad= ical equations are equations with the unknown x under = the radical.
Radical Equation= s
------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0065.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Radical Equations
Rad= ical equations are equations with the unknown x under = the radical.
To solve radical equation= s, we use the following fact.
Radical Equation= s
------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0066.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Radical Equations
Rad= ical equations are equations with the unknown x under = the radical.
To solve radical equations, we = use the following fact.
        = ;            &n= bsp;            If L=3DR, then L2<= span lang=3DEN-US style=3D'mso-fareast-font-family:\5B8B\4F53;mso-hansi-font-fa= mily: Arial;font-size:133%;color:red;mso-fareast-language:ZH-CN'> =3D R2. = ;
Radical Equation= s
------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0067.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Radical Equations
Rad= ical equations are equations with the unknown x under = the radical.
To solve radical equations, we = use the following fact.
        = ;            &n= bsp;            If L=3DR, then L2<= span lang=3DEN-US style=3D'mso-fareast-font-family:\5B8B\4F53;mso-hansi-font-fa= mily: Arial;font-size:133%;color:red;mso-fareast-language:ZH-CN'> =3D R2. = ;
Radical Equation= s
To solve a radical equation, square each side of the equation <= span style=3D'position:absolute;top:36.75%;left:5.24%;width:91.57%;height:5.25%= '>(repeatedly if necessary)= to remove the radicals.  =
------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0068.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Radical Equations
Rad= ical equations are equations with the unknown x under = the radical.
To solve radical equations, we = use the following fact.
        = ;            &n= bsp;            If L=3DR, then L2<= span lang=3DEN-US style=3D'mso-fareast-font-family:\5B8B\4F53;mso-hansi-font-fa= mily: Arial;font-size:133%;color:red;mso-fareast-language:ZH-CN'> =3D R2. = ;
Radical Equation= s
To solve a radical equation, square each side of the equation <= span style=3D'position:absolute;top:36.75%;left:5.24%;width:107.49%;height:5.25= %'>(repeatedly if necessary)= to remove the radicals.  Then so= lve for x and check the answe= rs.
------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0069.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Radical Equations
Rad= ical equations are equations with the unknown x under = the radical.
To solve radical equations, we = use the following fact.
        = ;            &n= bsp;            If L=3DR, then L2<= span lang=3DEN-US style=3D'mso-fareast-font-family:\5B8B\4F53;mso-hansi-font-fa= mily: Arial;font-size:133%;color:red;mso-fareast-language:ZH-CN'> =3D R2. = ;
Radical Equation= s
To solve a radical equation, square each side of the equation <= span style=3D'position:absolute;top:36.75%;left:5.24%;width:107.49%;height:5.25= %'>(repeatedly if necessary)= to remove the radicals.  Then so= lve for x and check the answe= rs.
Example A. Solve.
<= span style=3D'font-size:133%;color:#003300'>a.Öx =3D 4
------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0069_image001.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAN AAEAgAAAAAAzAAIDjI9XADt= ------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0070.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Radical Equations
Rad= ical equations are equations with the unknown x under = the radical.
To solve radical equations, we = use the following fact.
        = ;            &n= bsp;            If L=3DR, then L2<= span lang=3DEN-US style=3D'mso-fareast-font-family:\5B8B\4F53;mso-hansi-font-fa= mily: Arial;font-size:133%;color:red;mso-fareast-language:ZH-CN'> =3D R2. = ;
Radical Equation= s
To solve a radical equation, square each side of the equation <= span style=3D'position:absolute;top:36.75%;left:5.24%;width:107.49%;height:5.25= %'>(repeatedly if necessary)= to remove the radicals.  Then so= lve for x and check the answe= rs.
Example A. Solve.
<= span style=3D'font-size:133%;color:#003300'>a.Öx =3D 4        = ;    square each side
------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0070_image002.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAN AAEAgAAAAAAzAAIDjI9XADt= ------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0071.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Radical Equations
Rad= ical equations are equations with the unknown x under = the radical.
To solve radical equations, we = use the following fact.
        = ;            &n= bsp;            If L=3DR, then L2<= span lang=3DEN-US style=3D'mso-fareast-font-family:\5B8B\4F53;mso-hansi-font-fa= mily: Arial;font-size:133%;color:red;mso-fareast-language:ZH-CN'> =3D R2. = ;
Radical Equation= s
To solve a radical equation, square each side of the equation <= span style=3D'position:absolute;top:36.75%;left:5.24%;width:107.49%;height:5.25= %'>(repeatedly if necessary)= to remove the radicals.  Then so= lve for x and check the answe= rs.
Example A. Solve.
<= span style=3D'font-size:133%;color:#003300'>a.Öx =3D 4        = ;    square each side  = ;
    (Öx)2 =3D 42
------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0071_image003.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAN AAEAgAAAAAAzAAIDjI9XADt= ------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0071_image004.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAJ AAEAgAAAAAAzAAIDjH8FADs= ------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0072.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Radical Equations
Rad= ical equations are equations with the unknown x under = the radical.
To solve radical equations, we = use the following fact.
        = ;            &n= bsp;            If L=3DR, then L2<= span lang=3DEN-US style=3D'mso-fareast-font-family:\5B8B\4F53;mso-hansi-font-fa= mily: Arial;font-size:133%;color:red;mso-fareast-language:ZH-CN'> =3D R2. = ;
Radical Equation= s
To solve a radical equation, square each side of the equation <= span style=3D'position:absolute;top:36.75%;left:5.24%;width:107.49%;height:5.25= %'>(repeatedly if necessary)= to remove the radicals.  Then so= lve for x and check the answe= rs.
Example A. Solve.
<= span style=3D'font-size:133%;color:#003300'>a.Öx =3D 4        = ;    square each side  = ;
    (Öx)2 =3D 42
        = ;  x =3D 16
------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0072_image005.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAN AAEAgAAAAAAzAAIDjI9XADt= ------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0072_image006.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAJ AAEAgAAAAAAzAAIDjH8FADs= ------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0073.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Radical Equations
Rad= ical equations are equations with the unknown x under = the radical.
To solve radical equations, we = use the following fact.
        = ;            &n= bsp;            If L=3DR, then L2<= span lang=3DEN-US style=3D'mso-fareast-font-family:\5B8B\4F53;mso-hansi-font-fa= mily: Arial;font-size:133%;color:red;mso-fareast-language:ZH-CN'> =3D R2. = ;
Radical Equation= s
To solve a radical equation, square each side of the equation <= span style=3D'position:absolute;top:36.75%;left:5.24%;width:107.49%;height:5.25= %'>(repeatedly if necessary)= to remove the radicals.  Then so= lve for x and check the answe= rs.
Example A. Solve.
<= span style=3D'font-size:133%;color:#003300'>a.Öx =3D 4        = ;    square each side  = ;
    (Öx)2 =3D 42
        = ;  x =3D 16    &n= bsp; It works.
------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0073_image007.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAN AAEAgAAAAAAzAAIDjI9XADt= ------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0073_image008.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAJ AAEAgAAAAAAzAAIDjH8FADs= ------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0074.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Radical Equations
Rad= ical equations are equations with the unknown x under = the radical.
To solve radical equations, we = use the following fact.
        = ;            &n= bsp;            If L=3DR, then L2<= span lang=3DEN-US style=3D'mso-fareast-font-family:\5B8B\4F53;mso-hansi-font-fa= mily: Arial;font-size:133%;color:red;mso-fareast-language:ZH-CN'> =3D R2. = ;
Radical Equation= s
To solve a radical equation, square each side of the equation <= span style=3D'position:absolute;top:36.75%;left:5.24%;width:107.49%;height:5.25= %'>(repeatedly if necessary)= to remove the radicals.  Then so= lve for x and check the answe= rs.
Example A. Solve.
<= span style=3D'font-size:133%;color:#003300'>a.Öx =3D 4        = ;    square each side  = ;
    (Öx)2 =3D 42
        = ;  x =3D 16    &n= bsp; It works.
b. Öx – 3  =3D 4
------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0074_image009.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAo AAEAgAAAAAAzAAIFjI+py1gAO1== ------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0074_image010.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAN AAEAgAAAAAAzAAIDjI9XADt= ------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0074_image011.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAJ AAEAgAAAAAAzAAIDjH8FADs= ------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0075.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Radical Equations
Rad= ical equations are equations with the unknown x under = the radical.
To solve radical equations, we = use the following fact.
        = ;            &n= bsp;            If L=3DR, then L2<= span lang=3DEN-US style=3D'mso-fareast-font-family:\5B8B\4F53;mso-hansi-font-fa= mily: Arial;font-size:133%;color:red;mso-fareast-language:ZH-CN'> =3D R2. = ;
Radical Equation= s
To solve a radical equation, square each side of the equation <= span style=3D'position:absolute;top:36.75%;left:5.24%;width:107.49%;height:5.25= %'>(repeatedly if necessary)= to remove the radicals.  Then so= lve for x and check the answe= rs.
Example A. Solve.
<= span style=3D'font-size:133%;color:#003300'>a.Öx =3D 4        = ;    square each side  = ;
    (Öx)2 =3D 42
        = ;  x =3D 16    &n= bsp; It works.
b. Öx – 3  =3D 4     square each sid= e
------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0075_image012.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAo AAEAgAAAAAAzAAIFjI+py1gAO1== ------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0075_image013.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAN AAEAgAAAAAAzAAIDjI9XADt= ------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0075_image014.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAJ AAEAgAAAAAAzAAIDjH8FADs= ------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0076.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Radical Equations
Rad= ical equations are equations with the unknown x under = the radical.
To solve radical equations, we = use the following fact.
        = ;            &n= bsp;            If L=3DR, then L2<= span lang=3DEN-US style=3D'mso-fareast-font-family:\5B8B\4F53;mso-hansi-font-fa= mily: Arial;font-size:133%;color:red;mso-fareast-language:ZH-CN'> =3D R2. = ;
Radical Equation= s
To solve a radical equation, square each side of the equation <= span style=3D'position:absolute;top:36.75%;left:5.24%;width:107.49%;height:5.25= %'>(repeatedly if necessary)= to remove the radicals.  Then so= lve for x and check the answe= rs.
Example A. Solve.
<= span style=3D'font-size:133%;color:#003300'>a.Öx =3D 4        = ;    square each side  = ;
    (Öx)2 =3D 42
        = ;  x =3D 16    &n= bsp; It works.
b. Öx – 3  =3D 4     square each sid= e 
    (Öx – 3)2 =3D 42
------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0076_image015.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAo AAEAgAAAAAAzAAIFjI+py1gAO1== ------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0076_image016.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAN AAEAgAAAAAAzAAIDjI9XADt= ------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0076_image017.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAJ AAEAgAAAAAAzAAIDjH8FADs= ------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0076_image018.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAp AAEAgAAAAAAzAAIFjI+py1kAO1== ------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0077.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Radical Equations
Rad= ical equations are equations with the unknown x under = the radical.
To solve radical equations, we = use the following fact.
        = ;            &n= bsp;            If L=3DR, then L2<= span lang=3DEN-US style=3D'mso-fareast-font-family:\5B8B\4F53;mso-hansi-font-fa= mily: Arial;font-size:133%;color:red;mso-fareast-language:ZH-CN'> =3D R2. = ;
Radical Equation= s
To solve a radical equation, square each side of the equation <= span style=3D'position:absolute;top:36.75%;left:5.24%;width:107.49%;height:5.25= %'>(repeatedly if necessary)= to remove the radicals.  Then so= lve for x and check the answe= rs.
Example A. Solve.
<= span style=3D'font-size:133%;color:#003300'>a.Öx =3D 4        = ;    square each side  = ;
    (Öx)2 =3D 42
        = ;  x =3D 16    &n= bsp; It works.
b. Öx – 3  =3D 4     square each sid= e 
    (Öx – 3)2 =3D 42        = ;  
     x – 3 =3D= 16
        = ;   x =3D 19
------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0077_image019.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAo AAEAgAAAAAAzAAIFjI+py1gAO1== ------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0077_image020.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAN AAEAgAAAAAAzAAIDjI9XADt= ------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0077_image021.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAJ AAEAgAAAAAAzAAIDjH8FADs= ------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0077_image022.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAp AAEAgAAAAAAzAAIFjI+py1kAO1== ------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0078.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Radical Equations
Rad= ical equations are equations with the unknown x under = the radical.
To solve radical equations, we = use the following fact.
        = ;            &n= bsp;            If L=3DR, then L2<= span lang=3DEN-US style=3D'mso-fareast-font-family:\5B8B\4F53;mso-hansi-font-fa= mily: Arial;font-size:133%;color:red;mso-fareast-language:ZH-CN'> =3D R2. = ;
Radical Equation= s
To solve a radical equation, square each side of the equation <= span style=3D'position:absolute;top:36.75%;left:5.24%;width:107.49%;height:5.25= %'>(repeatedly if necessary)= to remove the radicals.  Then so= lve for x and check the answe= rs.
Example A. Solve.
<= span style=3D'font-size:133%;color:#003300'>a.Öx =3D 4        = ;    square each side  = ;
    (Öx)2 =3D 42
        = ;  x =3D 16    &n= bsp; It works.
b. Öx – 3  =3D 4     square each sid= e 
    (Öx – 3)2 =3D 42        = ;  
     x – 3 =3D= 16
        = ;   x =3D 19     <= /span>It works.
------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0078_image023.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAo AAEAgAAAAAAzAAIFjI+py1gAO1== ------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0078_image024.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAN AAEAgAAAAAAzAAIDjI9XADt= ------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0078_image025.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAJ AAEAgAAAAAAzAAIDjH8FADs= ------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0078_image026.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAp AAEAgAAAAAAzAAIFjI+py1kAO1== ------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0063.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Radical Equations
c. Ö2x + 1 =3D –3<= /div>
Radical Equation= s
------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0063_image027.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhLwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAt AAEAgAAAAAAzAAIFjI+py10AO1== ------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0079.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Radical Equations
c. Ö2x + 1 =3D –3        = ;   square each side
    (Ö2x + 1)2 =3D (–3)2
Radical Equation= s
------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0079_image028.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhLwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAt AAEAgAAAAAAzAAIFjI+py10AO1== ------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0079_image029.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhMwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAx AAEAgAAAAAAzAAIGjI+py40FADs= ------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0081.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Radical Equations
c. Ö2x + 1 =3D –3        = ;   square each side
    (Ö2x + 1)2 =3D (–3)2
        2x + 1 =3D 9
Radical Equation= s
------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0081_image030.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhLwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAt AAEAgAAAAAAzAAIFjI+py10AO1== ------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0081_image031.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhMwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAx AAEAgAAAAAAzAAIGjI+py40FADs= ------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0082.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Radical Equations
c. Ö2x + 1 =3D –3        = ;   square each side
    (Ö2x + 1)2 =3D (–3)2
        2x + 1 =3D 9
2x =3D 8
Radical Equation= s
------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0082_image032.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhLwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAt AAEAgAAAAAAzAAIFjI+py10AO1== ------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0082_image033.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhMwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAx AAEAgAAAAAAzAAIGjI+py40FADs= ------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0083.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Radical Equations
c. Ö2x + 1 =3D –3        = ;   square each side
    (Ö2x + 1)2 =3D (–3)2
        2x + 1 =3D 9
2x =3D 8=
  x =3D 4
Radical Equation= s
------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0083_image034.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhLwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAt AAEAgAAAAAAzAAIFjI+py10AO1== ------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0083_image035.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhMwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAx AAEAgAAAAAAzAAIGjI+py40FADs= ------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0084.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Radical Equations
c. Ö2x + 1 =3D –3        = ;   square each side
    (Ö2x + 1)2 =3D (–3)2
        2x + 1 =3D 9
2x =3D 8=
  x =3D 4
However, x =3D 4 does not work. So there is no solution.
Radical Equation= s
------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0084_image036.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhLwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAt AAEAgAAAAAAzAAIFjI+py10AO1== ------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0084_image037.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhMwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAx AAEAgAAAAAAzAAIGjI+py40FADs= ------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0085.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Radical Equations
c. Ö2x + 1 =3D –3        = ;   square each side
    (Ö2x + 1)2 =3D (–3)2
        2x + 1 =3D 9
2x =3D 8=
  x =3D 4
However, x =3D 4 does not work. So there is no solution.
Radical Equation= s
For some problems, we have to square more than once to eliminate all the radical= s.
------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0085_image038.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhLwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAt AAEAgAAAAAAzAAIFjI+py10AO1== ------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0085_image039.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhMwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAx AAEAgAAAAAAzAAIGjI+py40FADs= ------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0086.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Radical Equations
c. Ö2x + 1 =3D –3        = ;   square each side
    (Ö2x + 1)2 =3D (–3)2
        2x + 1 =3D 9
2x =3D 8=
  x =3D 4
However, x =3D 4 does not work. So there is no solution.
Radical Equation= s
For some problems, we have to square more than once to eliminate all the radical= s. Recall the squaring formula that
(A ± B) = à A2 ± 2AB + B2
------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0086_image040.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhLwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAt AAEAgAAAAAAzAAIFjI+py10AO1== ------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0086_image041.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhMwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAx AAEAgAAAAAAzAAIGjI+py40FADs= ------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0087.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Radical Equations
c. Ö2x + 1 =3D –3        = ;   square each side
    (Ö2x + 1)2 =3D (–3)2
        2x + 1 =3D 9
2x =3D 8=
  x =3D 4
However, x =3D 4 does not work. So there is no solution.
Radical Equation= s
Example B. Expand.
a. (Öx + 4)2
For some problems, we have to square more than once to eliminate all the radical= s. Recall the squaring formula that
(A ± B) = à A2 ± 2AB + B2
------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0087_image042.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhLwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAt AAEAgAAAAAAzAAIFjI+py10AO1== ------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0087_image043.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhMwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAx AAEAgAAAAAAzAAIGjI+py40FADs= ------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0087_image044.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAJ AAEAgAAAAAAzAAIDjH8FADs= ------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0088.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Radical Equations
c. Ö2x + 1 =3D –3        = ;   square each side
    (Ö2x + 1)2 =3D (–3)2
        2x + 1 =3D 9
2x =3D 8=
  x =3D 4
However, x =3D 4 does not work. So there is no solution.
Radical Equation= s
Example B. Expand.
a. (Öx + 4)2     =3D (Ö= x )2 + 2 * 4 Öx + 42
For some problems, we have to square more than once to eliminate all the radical= s. Recall the squaring formula that
(A ± B) = à A2 ± 2AB + B2
------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0088_image045.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhLwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAt AAEAgAAAAAAzAAIFjI+py10AO1== ------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0088_image046.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhMwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAx AAEAgAAAAAAzAAIGjI+py40FADs= ------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0088_image047.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAJ AAEAgAAAAAAzAAIDjH8FADs= ------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0088_image048.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAJ AAEAgAAAAAAzAAIDjH8FADs= ------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0088_image049.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAK AAEAgAAAAAAzAAIDjI8FADs= ------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0089.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Radical Equations
c. Ö2x + 1 =3D –3        = ;   square each side
    (Ö2x + 1)2 =3D (–3)2
        2x + 1 =3D 9
2x =3D 8=
  x =3D 4
However, x =3D 4 does not work. So there is no solution.
Radical Equation= s
Example B. Expand.
a. (Öx + 4)2     =3D (Ö= x )2 + 2 * 4 Öx + 42
     =3D    x + 8Ö= x + 16
For some problems, we have to square more than once to eliminate all the radical= s. Recall the squaring formula that
(A ± B) = à A2 ± 2AB + B2
------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0089_image050.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhLwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAt AAEAgAAAAAAzAAIFjI+py10AO1== ------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0089_image051.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhMwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAx AAEAgAAAAAAzAAIGjI+py40FADs= ------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0089_image052.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAJ AAEAgAAAAAAzAAIDjH8FADs= ------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0089_image053.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAJ AAEAgAAAAAAzAAIDjH8FADs= ------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0089_image054.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAK AAEAgAAAAAAzAAIDjI8FADs= ------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0089_image055.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAAAK AAEAgAAAAAAzAAIDjI8FADs= ------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0062.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Radical Equations
Radical Equation= s
b. (Ö2x + 1 R= 11; 3)2
------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0062_image056.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhLgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAAAu AAEAgAAAAAAzAAIGjI+pyx0FADs= ------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0090.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Radical Equations
Radical Equation= s
b. (Ö2x + 1 R= 11; 3)2 
  &= nbsp; =3D (Ö2x + 1) – 2*3Ö2x + 1 + 3=
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Radical Equation= s
b. (Ö2x + 1 R= 11; 3)2 
  &= nbsp; =3D (Ö2x + 1) – 2*3Ö2x + 1 + 3=   &= nbsp; =3D  2x + 1 – 6<= /span>Ö= 2x + 1 + 9
------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0091_image059.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhLgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAAAu AAEAgAAAAAAzAAIGjI+pyx0FADs= ------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0091_image060.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhowACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAACg AAEAgAAAAAAzAAIQjI+pyw0Po5y02otl27ybAgA7 ------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0091_image061.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhLgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAs AAEAgAAAAAAzAAIFjI+py1wAO1== ------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0092.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Radical Equations
Radical Equation= s
b. (Ö2x + 1 R= 11; 3)2 
  &= nbsp; =3D (Ö2x + 1) – 2*3Ö2x + 1 + 3=   &= nbsp; =3D  2x + 1 – 6<= /span>Ö= 2x + 1 + 9
  &= nbsp; =3D 2x + 10 – 6Ö2x+1      
------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0092_image062.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhLgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAAAu AAEAgAAAAAAzAAIGjI+pyx0FADs= ------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0092_image063.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhowACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAACg AAEAgAAAAAAzAAIQjI+pyw0Po5y02otl27ybAgA7 ------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0092_image064.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhLgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAs AAEAgAAAAAAzAAIFjI+py1wAO1== ------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0092_image065.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAo AAEAgAAAAAAzAAIFjI+py1gAO1== ------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0104.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Radical Equations
Radical Equation= s
b. (Ö2x + 1 R= 11; 3)2 
  &= nbsp; =3D (Ö2x + 1) – 2*3Ö2x + 1 + 3=   &= nbsp; =3D  2x + 1 – 6<= /span>Ö= 2x + 1 + 9
  &= nbsp; =3D 2x + 10 – 6Ö2x+1      
When squa= ring both sides of an equation to remove a radical, = make sure= that radical term is isolated to one side first.
------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0104_image066.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhLgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAs AAEAgAAAAAAzAAIFjI+py1wAO1== ------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0104_image067.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhowACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAACh AAEAgAAAAAAzAAIQjI+pyw0Po5y02otj27yjAgA7 ------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0104_image068.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhLgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAAAu AAEAgAAAAAAzAAIGjI+pyx0FADs= ------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0104_image069.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAp AAEAgAAAAAAzAAIFjI+py1kAO1== ------=_NextPart_01C96AEC.5B425630 Content-Location: file:///C:/09764A33/1RadicalEquations_files/slide0105.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Radical Equations
Radical Equation= s
b. (Ö2x + 1 R= 11; 3)2 
  &= nbsp; =3D (Ö2x + 1) – 2*3Ö2x + 1 + 3=   &= nbsp; =3D  2x + 1 – 6<= /span>Ö= 2x + 1 + 9
  &= nbsp; =3D 2x + 10 – 6Ö2x+1      
Example C. Solve for x.
= a.Öx + 4  =3D Ö5x + 4
When squa= ring both sides of an equation to remove a radical, = make sure= that radical term is isolated to one side first.
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Radical Equation= s
b. (Ö2x + 1 R= 11; 3)2 
  &= nbsp; =3D (Ö2x + 1) – 2*3Ö2x + 1 + 3=   &= nbsp; =3D  2x + 1 – 6<= /span>Ö= 2x + 1 + 9
  &= nbsp; =3D 2x + 10 – 6Ö2x+1      
Example C. Solve for x.
a.Öx + 4  =3D Ö5x + 4        = ;            &n= bsp;       square both sides
    (Öx + 4)2 =3D (Ö5x + 4 )2
When squa= ring both sides of an equation to remove a radical, = make sure= that radical term is isolated to one side first.
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Radical Equation= s
b. (Ö2x + 1 R= 11; 3)2 
  &= nbsp; =3D (Ö2x + 1) – 2*3Ö2x + 1 + 3=   &= nbsp; =3D  2x + 1 – 6<= /span>Ö= 2x + 1 + 9
  &= nbsp; =3D 2x + 10 – 6Ö2x+1      
Example C. Solve for x.
a.Öx + 4  =3D Ö5x + 4        = ;            &n= bsp;       square both sides
    (Öx + 4)2 =3D (Ö5x + 4 )2 
    x + 2*4 Öx + 16  =3D 5x + 4
When squa= ring both sides of an equation to remove a radical, = make sure= that radical term is isolated to one side first.
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Radical Equation= s
b. (Ö2x + 1 R= 11; 3)2 
  &= nbsp; =3D (Ö2x + 1) – 2*3Ö2x + 1 + 3=   &= nbsp; =3D  2x + 1 – 6<= /span>Ö= 2x + 1 + 9
  &= nbsp; =3D 2x + 10 – 6Ö2x+1      
Example C. Solve for x.
a.Öx + 4  =3D Ö5x + 4        = ;            &n= bsp;       square both sides
    (Öx + 4)2 =3D (Ö5x + 4 )2 
    x + 2*4 Öx + 16  =3D 5x += 4        = ;         isolate the radical
When squa= ring both sides of an equation to remove a radical, = make sure= that radical term is isolated to one side first.
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Radical Equation= s
b. (Ö2x + 1 R= 11; 3)2 
  &= nbsp; =3D (Ö2x + 1) – 2*3Ö2x + 1 + 3=   &= nbsp; =3D  2x + 1 – 6<= /span>Ö= 2x + 1 + 9
  &= nbsp; =3D 2x + 10 – 6Ö2x+1      
Example C. Solve for x.
a.Öx + 4  =3D Ö5x + 4        = ;            &n= bsp;       square both sides
    (Öx + 4)2 =3D (Ö5x + 4 )2 
    x + 2*4 Öx + 16  =3D 5x + 4        = ;         isolate the radical
        = ;           8Öx  =3D  4x – 12
When squa= ring both sides of an equation to remove a radical, = make sure= that radical term is isolated to one side first.
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Radical Equation= s
b. (Ö2x + 1 R= 11; 3)2 
  &= nbsp; =3D (Ö2x + 1) – 2*3Ö2x + 1 + 3=   &= nbsp; =3D  2x + 1 – 6<= /span>Ö= 2x + 1 + 9
  &= nbsp; =3D 2x + 10 – 6Ö2x+1      
Example C. Solve for x.
a.Öx + 4  =3D Ö5x + 4        = ;            &n= bsp;       square both sides
    (Öx + 4)2 =3D (Ö5x + 4 )2 
    x + 2*4 Öx + 16  =3D 5x + 4        = ;         isolate the radical
        = ;           8Öx  =3D  4x – 12        = ;         divide by 4
When squa= ring both sides of an equation to remove a radical, = make sure= that radical term is isolated to one side first.
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Radical Equation= s
b. (Ö2x + 1 R= 11; 3)2 
  &= nbsp; =3D (Ö2x + 1) – 2*3Ö2x + 1 + 3=   &= nbsp; =3D  2x + 1 – 6<= /span>Ö= 2x + 1 + 9
  &= nbsp; =3D 2x + 10 – 6Ö2x+1      
Example C. Solve for x.
a.Öx + 4  =3D Ö5x + 4        = ;            &n= bsp;       square both sides
    (Öx + 4)2 =3D (Ö5x + 4 )2 
    x + 2*4 Öx + 16  =3D 5x + 4        = ;         isolate the radical
        = ;           8Öx  =3D  4x – 12        = ;         divide by 4
        = ;            2Öx  =3D x – 3
When squa= ring both sides of an equation to remove a radical, = make sure= that radical term is isolated to one side first.
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